Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813621 | C2 | semidirect |
| 3. #20298892 | C2 | semidirect |
| 4. #20298887 | C2 | semidirect |
| 5. #20298882 | C2 | semidirect |
| 6. #20298877 | C2 | semidirect |
| 7. #20298641 | C2 | semidirect |
| 8. #20298621 | C2 | semidirect |
| 11. #428×C113 | C2 | semidirect |
| 44. #14268647 | Q8 | semidirect |
| 104. D452 | C2×Q8 | semidirect |
| 111. Dic226 | C2×Q8 | semidirect |
| 139. C113 | #3079 | semidirect |
| 147. #428 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813621 | 2 |
| #20299066 | 2 |
| #20298892 | 2 |
| #20298887 | 2 |
| #20298882 | 2 |
| #20298877 | 2 |
| #20298641 | 2 |
| #20298621 | 2 |
| #20298600 | 2 |
| #20298597 | 2 |
| #428×C113 | 2 |
| #3079 | 113 |